Third-order theory of spectacle lenses applied to correction of peripheral refractive errors

Purpose: To demonstrate that relatively simple third-order theory can provide a framework which shows how peripheral refraction can be manipulated by altering the forms of spectacle lenses. Method: Third-order equations were used to yield lens forms that correct peripheral power errors, either for the lenses alone or in combination with typical peripheral refractions of myopic eyes. These results were compared with those of finite ray-tracing. Results: The approximate forms of spherical and conicoidal lenses provided by third-order theory were flatter over a moderate myopic range than the forms obtained by rigorous raytracing. Lenses designed to correct peripheral refractive errors produced large errors when used with foveal vision and a rotating eye. Correcting astigmatism tended to give large errors in mean oblique error and vice versa. When only spherical lens forms are used, correction of the relative hypermetropic peripheral refractions of myopic eyes which are observed experimentally, or the provision of relative myopic peripheral refractions in such eyes, seems impossible in the majority of cases. Conclusion: The third-order spectacle lens design approach can readily be used to show trends in peripheral refraction.